Math Arguments

Floorlamp

The floor lamp casts a shadow.


Straight line AB is drawn on a wide, spacious floor. A lamp is at a height of 8m above point C, which is located on line AB. Line CD is perpendicular to line AB. A rectangular solid 5m by 3m by 4m is on the floor as shown. The box is 2m from line AB and a meters from line CD. Assume the lamp is a point source and will cast a perfect shadow. Given that the rectangular solid casts a shadow with area \(90m^2\), determine the distance a (in meters).

• Does the 2m distance from the wall matter to the shape of the shadow?


• How does the distance a change the area of the shadow?


• What shape is that shadow on the floor?


• Are the edges of the shadow guaranteed to parallel with the edges of the box?


• How far away is that box from the light?